## No trace type specified:
##   Based on info supplied, a 'scatter' trace seems appropriate.
##   Read more about this trace type -> https://plot.ly/r/reference/#scatter
## No trace type specified:
##   Based on info supplied, a 'bar' trace seems appropriate.
##   Read more about this trace type -> https://plot.ly/r/reference/#bar
data_0713 <- as.data.frame(date_covid19.mask("2020-07-13"))

mask.data_0713 <- lm(COVID_CASE_RATE ~ obs_mask + PERCENT_POSITIVE + POP_DENOMINATOR, data_0713)

nomask.data_0713 <- lm(COVID_CASE_RATE ~ PERCENT_POSITIVE + POP_DENOMINATOR, data_0713)
  
summary(mask.data_0713)
## 
## Call:
## lm(formula = COVID_CASE_RATE ~ obs_mask + PERCENT_POSITIVE + 
##     POP_DENOMINATOR, data = data_0713)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -706.90 -134.73   32.45  191.81  526.37 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -2.239e+02  7.313e+02  -0.306    0.766    
## obs_mask         -4.426e+02  7.788e+02  -0.568    0.582    
## PERCENT_POSITIVE  1.980e+02  2.772e+01   7.143 3.13e-05 ***
## POP_DENOMINATOR  -2.770e-04  6.201e-03  -0.045    0.965    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 392 on 10 degrees of freedom
## Multiple R-squared:  0.8978, Adjusted R-squared:  0.8672 
## F-statistic:  29.3 on 3 and 10 DF,  p-value: 2.88e-05
summary(nomask.data_0713)
## 
## Call:
## lm(formula = COVID_CASE_RATE ~ PERCENT_POSITIVE + POP_DENOMINATOR, 
##     data = data_0713)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -691.10  -64.02   32.04  212.52  563.41 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -5.646e+02  4.059e+02  -1.391    0.192    
## PERCENT_POSITIVE  2.069e+02  2.214e+01   9.344 1.45e-06 ***
## POP_DENOMINATOR  -2.520e-03  4.633e-03  -0.544    0.597    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 379.7 on 11 degrees of freedom
## Multiple R-squared:  0.8945, Adjusted R-squared:  0.8754 
## F-statistic: 46.66 on 2 and 11 DF,  p-value: 4.234e-06
anova(mask.data_0713, nomask.data_0713)
## Analysis of Variance Table
## 
## Model 1: COVID_CASE_RATE ~ obs_mask + PERCENT_POSITIVE + POP_DENOMINATOR
## Model 2: COVID_CASE_RATE ~ PERCENT_POSITIVE + POP_DENOMINATOR
##   Res.Df     RSS Df Sum of Sq      F Pr(>F)
## 1     10 1536593                           
## 2     11 1586234 -1    -49642 0.3231 0.5823
confint(mask.data_0713)
##                          2.5 %       97.5 %
## (Intercept)      -1.853277e+03 1.405406e+03
## obs_mask         -2.177823e+03 1.292549e+03
## PERCENT_POSITIVE  1.362476e+02 2.597779e+02
## POP_DENOMINATOR  -1.409353e-02 1.353952e-02
confint(nomask.data_0713)
##                          2.5 %       97.5 %
## (Intercept)      -1.458022e+03 3.288954e+02
## PERCENT_POSITIVE  1.581870e+02 2.556648e+02
## POP_DENOMINATOR  -1.271785e-02 7.677142e-03
autoplot(mask.data_0713)

autoplot(nomask.data_0713)